One way of viewing PCA is a reflection and rotation of the original coordinates, while keeping the points pairwise fixed.
For exposition purposes, take a data set in two dimensions with x and y positively correlated, this could result in a PCA with a 45 degrees anti-clockwise rotation.
It is the reflection part I do not understand. What do the reflections represent? What information does a reflection have that differs from the information content of a rotation? Wha is the difference between a reflection and the eigenvector directions?